# Math Help - Max Point

1. ## Max Point

A) Find the coordinates of the absolute maximum point for the curve

B) Write an equation for the set of absolute maximum points for the curves y=xe^(-kx) as k varies through positive values

Im not really sure where to start with this. It is a calc ab problem. I think i would start with the derivative which woule be -ke^(-kx)+e^(-kx). After that im not sure where to go

2. Originally Posted by calc_help123
A) Find the coordinates of the absolute maximum point for the curve

B) Write an equation for the set of absolute maximum points for the curves y=xe^(-kx) as k varies through positive values

Im not really sure where to start with this. It is a calc ab problem. I think i would start with the derivative which woule be -k x e^(-kx)+e^(-kx). Mr F says: No. You're missing the red x.

After that im not sure where to go
$0 = -k {\color{red}x} e^{-kx} + e^{-kx} \Rightarrow e^{-kx} (1 - kx) = 0 \Rightarrow x = \frac{1}{k}$.

Now you have to test the nature of this solution. Using the second derivative test might be the easiest way.

3. so when u plug the $\frac{1}{k}$ back in to the original equation you get $\frac{e^{\frac{-x}{k}}}{k}$ correct? but how would i tackle part b?

4. Originally Posted by OnMyWayToBeAMathProffesor
so when u plug the $\frac{1}{k}$ back in to the original equation you get $\frac{e^{\frac{-x}{k}}}{k}$ correct? but how would i tackle part b?
did you perform the second derivative test as recommended by Mr. F ?